Multi-machine four-dimensional cooperative path planning method for pre-calculating deviation path and dynamically re-planning

Abstract

The invention discloses a multi-machine four-dimensional cooperative path planning method for pre-calculating a deviation path and dynamically re-planning, and belongs to the field of cooperative control and path planning of unmanned aerial vehicle clusters. The method comprises the following steps: dividing a three-dimensional airspace into cubic empty blocks, constructing a directed connected graph, and removing the empty blocks and edges which do not meet a safe distance; generating an initial three-dimensional path of each unmanned aerial vehicle by using a dynamic priority fast expansion random tree algorithm; taking an end point empty block as a starting point, constructing a reverse reachable graph by means of breadth-first search, pre-calculating a plurality of deviation paths from a neighborhood empty block to an end point in an off-line manner, and storing the deviation paths into the empty block; when a dynamic threat is detected in the task, calling an improved heuristic artificial potential field algorithm to generate a local obstacle avoidance section; and retrieving a pre-stored deviation path after obstacle avoidance, and selecting an optimal path for splicing in combination with a cost function. According to the method, the calculation amount is moved forward to an offline stage, the dynamic environment re-planning time is shortened, simultaneous arrival of multiple machines and space safety are guaranteed, and the expansion capability and the real-time performance are improved.

Description

Technical Field

[0001] This invention belongs to the field of UAV path planning and swarm collaborative control technology, specifically involving a multi-aircraft four-dimensional collaborative path planning method with pre-calculated deviation paths and dynamic replanning. Background Technology

[0002] With the improvement of the performance and autonomous decision-making capabilities of unmanned aerial vehicle (UAV) platforms, multi-UAV collaborative missions have been widely used in scenarios such as military strikes, emergency rescue, and urban airspace inspection. The core requirement is to ensure no spatial collisions between UAVs in dynamic environments (such as sudden threats or temporary no-fly zones) while also meeting strict temporal coordination constraints (such as simultaneous arrival at the target point). However, existing multi-UAV path planning methods generally suffer from technical pain points such as high replanning costs, high response latency, and difficulty in spatiotemporal coordination in dynamic environments, making it difficult to meet the needs of practical applications.

[0003] Existing technologies can be mainly divided into three categories, each with significant drawbacks: Local collision avoidance methods (such as artificial potential fields and optimal reciprocal collision avoidance) are computationally efficient and can respond quickly to local dynamic changes, but they are prone to getting trapped in local minima (such as stagnation when surrounded by multiple obstacles), and they do not consider time coordination at all. Multiple drones often have significant differences in arrival time due to a lack of speed coordination, resulting in a loss of mission timeliness; Coupled planning methods (such as conflict search) can theoretically achieve global optimum, but their joint state space dimension increases exponentially with the number of drones. In multi-drone swarm scenarios, the planning time is too long, and the replanning delay further accumulates under dynamic threats, failing to meet the real-time response requirements; Decoupled planning methods (such as fixed priority planning) can balance efficiency and coordination to some extent, but they are prone to triggering a "replanning chain reaction" under dynamic threats (after one drone avoids an obstacle, multiple related drones need to replan), and the time window is difficult to reallocate, making it difficult to ensure that multiple drones arrive synchronously. The aforementioned shortcomings prevent existing methods from simultaneously addressing real-time performance and spatiotemporal coordination in dynamic environments, severely limiting the practical application value of multi-UAV swarms. There is an urgent need for a path planning scheme that is low-overhead, fast-response, and can guarantee time coordination. Summary of the Invention

[0004] To further meet the requirements of low overhead, fast response, and guaranteed time coordination, this invention proposes a multi-machine four-dimensional collaborative path planning method with pre-calculated deviation paths and dynamic replanning.

[0005] Includes the following steps:

[0006] Step 1: 3D Spatial Domain Modeling and Spatial Block Partitioning: Divide the given bounded 3D spatial domain into regular meshes, discretizing the spatial domain into several blocks with side lengths of... The cube contains empty blocks; each empty block is assigned a unique triplet integer index as its identifier, used to locate the block where the drone is located; based on the center coordinates of the empty block and the preset maximum edge length... First, establish directed connectivity between adjacent empty blocks by constructing a directed graph in the spatial domain. ,in, For vertex set, For edge set, It is an adjacency structure;

[0007] Step 2, Safety Constraint Processing: Based on the spatial location and safety radius of static obstacles and no-fly zones, empty blocks and their associated directed edges that are less than the safety threshold from static obstacles or no-fly zones are eliminated. Furthermore, based on the influence radius and existence time window of dynamic threats (such as radar, missiles, and other mobile or temporarily appearing dangerous targets in the battlefield environment), empty blocks located within the influence area are marked as dynamically dangerous empty blocks within the corresponding time interval, prohibiting their passage during that time interval. Simultaneously, spatial and temporal coordinated safety constraints are set: minimum safe distance between aircraft. ( , For different drone paths), minimum time interval between drones ( , (where the path segment timestamp) The function for calculating Euclidean distance. , Global paths for two different drones This is the minimum safe distance threshold between machines (unit: m). For drones Timestamp of the corresponding path segment For drones The timestamps of the corresponding path segments (both are time stamps of path segments in the same spatially similar region, in seconds). The minimum time interval threshold between machines (unit: seconds);

[0008] Step 3: Initial Path Generation: Considering only static obstacles and no-fly zone constraints, for each UAV, using its starting empty block and target empty block as boundary conditions, the Dynamic Priority Fast Expanding Random Tree (DPRRT*) algorithm is used to generate a three-dimensional path from the starting point to the ending point, and each path point is stored in the path information table of the corresponding empty block to form an initial four-dimensional path set for multi-UAV collaboration.

[0009] Step 4, Reverse Reachability Graph Construction: Starting with the target empty block Starting from a node, a breadth-first search is performed on the directed graph in the airspace in the opposite direction to the flight direction. Under the premise of satisfying static safety constraints (static obstacle constraints and no-fly zone constraints), the search expands layer by layer to include predecessor blocks that can reach the target block. That is, through the logic of "backtracking from the endpoint," all feasible regions that can reach the target are pre-locked, providing a basis for subsequent path pre-calculation and selection, and constructing a reverse reachability graph. The reverse reachability graph is defined as follows: , It is a reverse reachability graph, and its core function is to store all feasible paths that can reach the target empty block and their corresponding starting empty blocks; It refers to the common endpoint empty block of a multi-drone collaborative mission; It refers to a feasible path, representing a continuous trajectory from a certain empty block to the target empty block; Let be the i-th empty block, and let be any empty block in the reverse reachability graph that can reach the destination empty block. Based on the above steps, the constructed reverse reachability graph can record the reachability status of each empty block to the target empty block and the identifier of reusable path segments.

[0010] Step 5, Offset Path Pre-calculation: For each initial path obtained in Step 3, traverse each path point in reverse chronological order from the endpoint to the starting point. Select a set of empty neighboring blocks to be expanded around the empty block where each point is located, based on a preset neighborhood radius. (in Let k be the set of empty neighboring blocks to be expanded for the k-th central empty block. Let d be a candidate empty block in the neighborhood, and d be a unique index of the candidate empty block. Candidate empty block The coordinates of the center of gravity For the central empty block The centroid coordinates, where k is the unique index of the central empty block. (where is the side length of the empty cube); after removing empty cubes not in the reverse reachable graph, an improved K-shortest path algorithm with temporal and threat costs is used to calculate multiple deviation paths from the candidate empty cubes to the target empty cube on the remaining candidate empty cubes; based on the comprehensive cost function: ,in The path's geometric length. To coordinate arrival at the reference time, To threaten exposure of penalties, , For adjustable weighting coefficients, the top K deviation paths with the lowest cost are selected as candidate path options and stored in the option set of the corresponding empty block. Each deviation path option contains at least the next hop empty block index, the expected arrival time, and the path point sequence indexed by time.

[0011] Step 6, Dynamic Threat Detection and Local Obstacle Avoidance: During mission execution, each UAV acquires dynamic threat information in real time based on onboard sensors or external perception systems. When the conditions are met... ( For drones Current state The function for calculating Euclidean distance. For dynamic threats in Spatial coordinates at time, The radius of influence of dynamic threats. When the safe radius of the drone is reached, the improved heuristic artificial potential field algorithm (IHAPF) is activated; this algorithm constructs a gravitational potential field. (Targeting the next reference path point on the global path) and adaptive repulsive potential field The resultant force control quantity is This drives the drone to deviate from its current path and move away from the threat source along a continuous trajectory until the obstacle avoidance end time and the corresponding empty block are recorded, forming a local obstacle avoidance segment.

[0012] Step 7: Path reconstruction and time coordination based on pre-calculated deviation paths: Calculate the remaining time for each UAV that has completed obstacle avoidance. ( To coordinate and reach the deadline, (At the end of obstacle avoidance), according to the urgency index The function for calculating Euclidean distance. Prioritize the urgency of path reconstruction for the k-th drone. Let k be the k-th drone that completes local obstacle avoidance, where k is the unique integer index of the drone in the drone swarm. For the k-th drone at the end of obstacle avoidance... state, For a common target empty block in a multi-drone collaborative mission, The drones are prioritized based on the remaining flight time from the obstacle avoidance time to the collaborative arrival deadline. Starting with the drone with the highest priority, the pre-stored path options are searched in the current empty block and its neighborhood. Candidate paths located in the reverse reachability graph are selected, and the deviation path with the lowest cost is selected based on the comprehensive cost function. The deviation path is then spliced ​​with the local obstacle avoidance segment in time order to obtain a new global path that satisfies the spatial and temporal collaborative constraints.

[0013] Furthermore, in step 1, the vertex attributes of the directed graph in the spatial domain include the Euclidean distance from the center of the empty block to the target empty block and the threat exposure penalty term within the empty block. When performing path search and deviation path pre-calculation, the above attributes are used as heuristic evaluation indicators to accelerate search convergence and reduce the probability of crossing high-threat areas.

[0014] In step 3, the sampling and expansion process of the Dynamic Priority Rapid Expanding Random Tree Algorithm (DPRRT*) introduces a priority scheduling mechanism based on task urgency and path coupling. This mechanism optimizes the shortcomings of the traditional DPRRT* algorithm, which relies only on a single-dimensional priority and does not consider the path coupling characteristics of multiple drones. Specifically, it first integrates task urgency (negatively correlated with the remaining task time of the drone) and path coupling (positively correlated with the degree of overlap of multiple drone paths) into a core priority evaluation index, replacing the traditional single priority determination method, and prioritizing the allocation of better path resources to drones with high path coupling and tight remaining time.

[0015] Furthermore: the K-shortest path algorithm is improved as follows:

[0016] The improved K-shortest path algorithm is based on the traditional Yen algorithm. Addressing its shortcomings—repeatedly calculating path segments, generating all branches, lacking targeted pruning, using only geometric length as the cost metric, failing to consider multi-machine path conflicts, and only outputting path sequences—it utilizes reusable path segments in the reverse reachability graph, calculates local branches using Dijkstra's algorithm and concatenates them with the initial reverse path, double-prunes empty blocks not in the reverse reachability graph, and calculates the comprehensive cost by combining geometric length, collaborative arrival time deviation weights, and threat exposure penalties. It also adds inter-machine spatiotemporal conflict verification and stores path options containing key information such as empty block indices and estimated arrival times. Finally, the top K optimal paths are selected and stored in their corresponding empty blocks. This reduces time complexity, minimizes invalid computation, adapts to the time constraints and security requirements of multi-machine collaboration, and reduces the pre-computation time complexity from the quadratic of the number of nodes to the product of the number of candidate paths and the average neighborhood size.

[0017] Furthermore: The improved K-shortest path algorithm is used to obtain K off-paths, specifically as follows:

[0018] First, by utilizing the constructed reverse reachability graph, the reusable path segments of each empty block recorded therein can be directly called to avoid repeated calculation of path segments and reduce basic overhead.

[0019] Secondly, for each selected candidate empty block, the local branch path to the next reverse path point is calculated using the Dijkstra algorithm, and then spliced ​​with the remaining part of the reverse initial path to form a complete deviation path. The complexity is further reduced by double pruning optimization, that is, reusing the path segments already recorded in the reverse reachability graph and pruning candidate empty blocks that are not in the reverse reachability graph.

[0020] Finally, the comprehensive cost is calculated by combining the geometric path length, the weight of the cooperative arrival reference time deviation, and the threat exposure penalty. At the same time, the spatiotemporal conflict between the path and the initial paths of other UAVs is verified to meet the inter-UAV safety constraints. The top K deviation paths with the lowest cost are selected as candidate path options and stored in the option set of the corresponding empty block.

[0021] Furthermore: Improvements are made to the Heuristic Artificial Potential Field (IHAPF) algorithm, specifically:

[0022] Based on the traditional artificial potential field algorithm, the gravitational potential field orientation is first optimized by adjusting the gravitational target from a distant empty block of the mission target to the next reference path point of the initial path in step 3. This ensures that the UAV does not deviate from the main mission line and avoids the inability to complete obstacle avoidance due to excessive gravity. Secondly, an adaptive repulsive potential field is designed, with the magnitude of the repulsive force dynamically adjusted according to the distance between the UAV and the dynamic threat. The closer the distance, the greater the repulsive force. After exceeding the safe range, the repulsive force decays to 0, solving the problem that traditional algorithms are prone to getting trapped in local minima. Next, a pre-stored path guidance constraint is embedded. During the obstacle avoidance process, the UAV is preferentially driven to move towards the empty block with the pre-stored deviation path option in step 5, ensuring that the pre-stored resources can be directly called after the obstacle avoidance is completed. Finally, a time coordination constraint is added to strictly control the flight time of the obstacle avoidance segment within the tolerance range of the coordinated arrival reference time, avoiding time deviations in subsequent path splicing.

[0023] Experimental results show that PC-DPRRT* significantly outperforms the baseline algorithms DPRRT* and CDH-PP in multi-UAV path planning in dynamic battlefield scenarios. Although there is some initial overhead in the preprocessing stage due to the construction of the reverse reachability graph and the pre-generated deviation path, by pruning unreachable empty blocks in advance, online planning only needs to query the pre-stored paths of the current empty block and its neighborhood, without the need for a global search. In terms of path planning time, after obstacle avoidance, PC-DPRRT* only needs to splice the obstacle avoidance segment and the pre-calculated deviation path and perform lightweight verification. It has the shortest median planning time with small fluctuations, which is an order of magnitude faster than the baseline algorithms. The advantage is even more significant when there are 12 UAVs. Regarding inter-drone deviation, PC-DPRRT* maintains low values ​​and low fluctuations across various drone numbers through dual screening of time matching and reachability, demonstrating time coordination far exceeding the baseline. In terms of mission success rate, PC-DPRRT* achieved 100% success in experiments with 1-12 drones, while the success rates of DPRRT* and CDH-PP decreased with increasing drone numbers. Path visualization further validates that in complex environments, only PC-DPRRT* enables all drones to reach the target synchronously after obstacle avoidance, while the baseline algorithm suffers from unreachable or conflicting paths, fully demonstrating the real-time performance, coordination, and reliability of PC-DPRRT*. Attached Figure Description

[0024] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0025] Figure 1 This is a framework diagram of the multi-machine four-dimensional collaborative path planning method with pre-calculated deviation path and dynamic replanning provided by the present invention;

[0026] Figure 2 This is a schematic diagram of a multi-UAV collaborative path planning scenario according to the present invention;

[0027] Figure 3 This is a schematic diagram showing the path planning results of the present invention and the comparison algorithm in the same scenario;

[0028] Figure 4 This is a schematic diagram comparing the preprocessing time of the present invention and the comparison algorithm under different numbers of drones;

[0029] Figure 5 This is a schematic diagram comparing the path planning time of the present invention and the comparison algorithm under different numbers of drones;

[0030] Figure 6 This is a schematic diagram comparing the arrival time deviation curves of the present invention and the comparison algorithm under different numbers of drones. Detailed Implementation

[0031] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0032] This invention provides a multi-machine four-dimensional collaborative path planning method that involves pre-calculating deviation paths and dynamic replanning.

[0033] refer to Figure 1 This invention employs a three-layer technical architecture of "offline preprocessing - deviation path pre-calculation - online real-time response." First, an initial path is generated using DPRRT*, completing four-dimensional environment modeling, no-fly zone calibration, and grid path information storage. Then, a reachability graph is constructed backwards from the target, and alternative deviation paths without spatiotemporal conflicts are pre-generated based on an improved Yen algorithm. In the online phase, sudden threats are detected in real time, and after rapid obstacle avoidance using the HAPF algorithm, pre-stored deviation paths are retrieved and their splicing verification and switching are completed. Simultaneously, spatiotemporal collaborative arrival by multiple UAVs is achieved, effectively solving the challenges of real-time performance, security, and collaboration in multi-UAV path planning under dynamic environments. An embodiment of this method is as follows:

[0034] Example:

[0035] A given bounded 3D spatial domain is partitioned into a regular grid, discretizing the spatial domain into several cubic blocks with side length . Each block is assigned a unique triplet integer index for locating the block where the UAV is located, and the center coordinates of the blocks are calculated. Based on the center coordinates of the blocks and the preset maximum edge length, directed connectivity relationships between adjacent blocks are established, constructing a directed graph of the spatial domain. ( For vertex set, For edge set, (For adjacency structure), see reference Figure 1 The "Spatial Domain Modeling and Indexing Module" uses the vertex attributes of the directed graph of the spatial domain, which include the Euclidean distance from the center of the empty block to the target empty block and the threat exposure penalty term within the empty block (set to 0.8 in the experiment). When performing path search and deviation path pre-calculation, the above attributes are used as heuristic evaluation indicators to accelerate search convergence and reduce the probability of crossing high-threat areas.

[0036] Based on the spatial location and safety radius of static obstacles and no-fly zones (Experimental design adapted for small to medium-sized drones), the distance to static obstacles or no-fly zones must meet the following requirements. ( For Euclidean distance, Empty blocks and their associated directed edges (considering static obstacles or no-fly zones) are culled; the impact radius of dynamic threats is also considered. (Experimental simulation of the kill range of anti-aircraft fire) and the time window in existence. Within the corresponding time interval, for those located within the affected area (meeting the following conditions) Empty blocks are marked as dynamic dangerous empty blocks, and passage is prohibited within this time interval, corresponding to the moving blue dynamic threat area in Figure 2 (multi-UAV collaborative scenario diagram); at the same time, spatial and temporal collaborative safety constraints are set: minimum safe distance between UAVs. ( , For different drone paths, ensure no collisions between drone trajectories as shown in Figure 2, and minimize the time interval between drones. ( , (Time point of the path segment).

[0037] Considering only static obstacles and no-fly zone constraints, for each UAV, using its starting and target empty blocks as boundary conditions, the Dynamic Priority Fast Expanding Random Tree (DPRRT*) algorithm is employed to generate a 3D path from the starting point to the ending point. (Refer to...) Figure 1 The "initial path generation module" of the algorithm introduces a priority scheduling mechanism based on task urgency and path coupling during the sampling and expansion process (in the experiment, task urgency is negatively correlated with the remaining task time of the UAV, and path coupling is positively correlated with the degree of overlap of multi-UAV paths, giving priority to assigning better paths to UAVs with high path coupling and tight remaining time (such as UAV C being the farthest from the target), and storing each path point in the path information table of the corresponding empty block to form an initial four-dimensional path set for multi-UAV collaboration.

[0038] target empty block Starting from a node, a breadth-first search is performed on the directed graph in the airspace along the direction opposite to the flight direction. Under the premise of satisfying static safety constraints, the search expands layer by layer to include predecessor blocks that can reach the target block. The reverse reachable graph is defined as... Meanwhile, the reverse reachability graph can record the reachability state and reusable paths from each empty block to the target empty block (in the experiment...). Figure 2 "Unreachable empty blocks" blocked by static obstacles are pruned in advance, reducing more than 30% of subsequent invalid calculations.

[0039] For each initial path obtained along DPRRT*, traverse each path point in reverse chronological order from the endpoint to the starting point, and select a set of empty neighboring blocks to be expanded around the empty block at each point according to a preset neighborhood radius. (In the experiment) (The neighborhood contains 6 adjacent empty blocks); after removing empty blocks not in the reverse reachability graph, an improved K-shortest path algorithm with temporal and threat costs is applied to the remaining candidate empty blocks (based on the traditional Yen algorithm; in the experiment, reusable paths recorded in the reverse reachability graph are directly reused for some paths, and candidate empty blocks not in the reverse reachability graph are pruned in advance, reducing the pre-computation time complexity from the square of the number of nodes). Reduced to the product of candidate path number and average neighborhood size ,in( , Calculate multiple deviation paths from the candidate empty block to the target empty block; based on the comprehensive cost function. in The path's geometric length. To coordinate arrival at the reference time, To mitigate the penalty for threat exposure, the top 5 deviation paths with the lowest cost are selected as path options and stored in the option set of the corresponding empty block. Each deviation path option contains at least the next-hop empty block index, the expected arrival time, and a time-indexed path point sequence. Figure 1 The "Online Path Switching" feature provides pre-stored resources.

[0040] During mission execution, each UAV acquires dynamic threat information in real time based on onboard sensors or external sensing systems, and when the conditions are met... At that time, the Improved Heuristic Artificial Potential Field (IHAPF) algorithm is initiated; this algorithm constructs a gravitational potential field. (Targeting the next reference path point on the global path) and adaptive repulsive potential field The resultant force control quantity is This drives the drone to deviate from its current path and move away from the threat source along a continuous trajectory (corresponding to...) Figure 2 The obstacle avoidance trajectory of UAV A is recorded until the obstacle avoidance end time and the corresponding empty block are recorded, forming a local obstacle avoidance segment;

[0041] Calculate the remaining time for each drone that has completed obstacle avoidance. ( To coordinate and reach the deadline, (At the end of obstacle avoidance), according to the urgency index Prioritize drones; starting with the highest priority drone, search pre-stored path options within the current empty block and its neighborhood, and filter candidate paths located in the reverse reachability graph. Experimental time tolerance. Based on the comprehensive cost function, the deviation path with the minimum cost is selected and concatenated with the local obstacle avoidance segment in chronological order to obtain a new global path. Figure 3 The optimized trajectory of PC-DPRRT* satisfies both spatial and temporal constraints.

[0042] Experimental results show that PC-DPRRT* significantly outperforms the baseline algorithms DPRRT* and CDH-PP in multi-UAV path planning in dynamic battlefield scenarios (see reference). Figures 3 to 6 Although the preprocessing stage incurs some initial overhead due to the construction of the reverse reachability graph and the pre-generated deviation path ( Figure 4 The preprocessing time comparison curves are shown for different numbers of drones. The PC-DPRRT* preprocessing time is slightly higher than the baseline (but this is an offline one-time calculation). However, by pruning unreachable empty blocks in advance, online planning only needs to query the pre-stored paths of the current empty block and its neighbors, without the need for a global search; in terms of path planning time, Figure 5 (Comparison curves of path planning time under different numbers of drones) show that PC-DPRRT* only needs to splice the obstacle avoidance segment and the pre-calculated deviation path after obstacle avoidance and perform lightweight verification. It has the shortest median planning time with small fluctuations, and is an order of magnitude faster than the baseline algorithm. The advantage is more significant when there are 12 drones. Regarding arrival time deviation, Figure 6 (Comparison curves of arrival time deviation under different numbers of drones) show that PC-DPRRT* maintains a small value and low fluctuation under various drone numbers through dual screening of time matching and reachability, and its time coordination is far superior to the baseline; in terms of mission success rate, PC-DPRRT* achieved 100% success in experiments with 1-12 drones, while the success rate of DPRRT* and CDH-PP decreased as the number of drones increased. Figure 3 (Diagram showing path results compared to the comparison algorithm) Further verification shows that in complex environments, only PC-DPRRT* can enable all UAVs to reach the target synchronously after obstacle avoidance. The baseline algorithm has problems such as being unable to reach the target or path conflict, which fully demonstrates the real-time performance, coordination and reliability of PC-DPRRT*.

[0043] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-machine four-dimensional collaborative path planning method with pre-calculated deviation paths and dynamic replanning, characterized in that, Includes the following steps: Step 1: 3D spatial domain modeling and empty block partitioning: Divide the given bounded 3D spatial domain into regular grids, discretizing the spatial domain into several cubic empty blocks; assign a unique triplet integer index to each empty block as an empty block identifier, used to locate the empty block where the UAV is located; establish directed connectivity between adjacent empty blocks based on the center coordinates of the empty blocks and the preset connecting edges, forming a directed graph of the spatial domain. Step 2, Safety Constraint Processing: Based on the spatial location and safety radius of static obstacles and no-fly zones, empty blocks and their associated directed edges that are less than the safety threshold from static obstacles or no-fly zones are removed. Based on the influence radius and existence time window of dynamic threats, empty blocks located within the influence area are marked as dynamic dangerous empty blocks within the corresponding time interval. At the same time, spatial and temporal coordinated safety constraints are set: minimum safe distance between aircraft and minimum time interval between aircraft. Step 3, Initial Path Generation: Under the condition of considering only static obstacles and no-fly zone constraints, the three-dimensional initial path from the starting point to the ending point is generated using the Dynamic Priority Fast Expanding Random Tree Algorithm (DPRRT*) with the starting empty block and the target empty block as boundary conditions. Each initial path point is stored in the path information table of the corresponding empty block to form a set of initial four-dimensional paths for multi-machine collaboration. Step 4: Construct a reverse reachability graph: starting with the target empty block. Starting from the endpoint, a breadth-first search is performed on the directed graph in the airspace in the opposite direction to the flight direction. Under the premise of satisfying static safety constraints, the search expands layer by layer to include predecessor blocks that can reach the target block. By backtracking from the endpoint, all feasible regions that can reach the target are pre-identified, providing a basis for subsequent path pre-calculation and selection, and thus constructing a reverse reachability graph. The reverse reachability graph is defined as follows: , It is a reverse reachability graph that stores all feasible paths that can reach the target empty block and their corresponding starting empty blocks; It refers to the common endpoint empty block of a multi-drone collaborative mission; It refers to a feasible path, representing a continuous trajectory from a certain empty block to the target empty block; It is the i-th empty block, and can be reached in reverse from any other empty block in the graph that leads to the final empty block; Step 5, Deviation Path Pre-calculation: Based on each initial path obtained in Step 3, traverse each path point in reverse order from the endpoint to the starting point in chronological order. Select a set of empty blocks to be expanded around the empty block where each point is located according to a preset neighborhood radius. After removing empty blocks that are not in the reverse reachability graph, use an improved K-shortest path algorithm with temporal and threat costs to calculate multiple deviation paths from the candidate empty blocks to the target empty block on the remaining candidate empty blocks. Based on the comprehensive cost function, select the top K deviation paths with the smallest cost as candidate path options and store them in the option set of the corresponding empty block. Each deviation path option contains at least the next hop empty block index, the expected arrival time, and the path point sequence indexed by time. Step 6, Dynamic Threat Detection and Local Obstacle Avoidance: During mission execution, each UAV acquires dynamic threat information in real time based on onboard sensors or external perception systems. When the conditions are met... ;in, For drones Current state The function for calculating Euclidean distance. For dynamic threats in Spatial coordinates at time, The radius of influence of dynamic threats. The safe radius of the drone is defined as follows: when the Euclidean distance between the drone's state position at time t and the position of the dynamic threat at time τ is less than the sum of the influence radius of the dynamic threat and the drone's safe radius, the improved heuristic artificial potential field algorithm IHAPF is used to drive the drone to deviate from the current path and move away from the threat source along a continuous trajectory until the obstacle avoidance end time and the corresponding empty block are recorded, forming a local obstacle avoidance segment. Step 7: Path reconstruction and time coordination based on pre-calculated deviation paths: Calculate the remaining time for each UAV that has completed obstacle avoidance, and prioritize the UAVs according to the urgency index; starting from the UAV with the highest priority, search the offline pre-stored candidate path options in the current empty block and its neighborhood, filter the candidate paths that the current path is located in the reverse reachability graph, select the deviation path with the lowest cost based on the comprehensive cost function, and splice it with the local obstacle avoidance segment in time order to obtain a new global path that satisfies the spatial and temporal coordination constraints.

2. The multi-machine four-dimensional collaborative path planning method based on pre-calculated deviation paths and dynamic replanning as described in claim 1, characterized in that: In step 1, the vertex attributes of the directed graph in the spatial domain include the Euclidean distance from the center of the empty block to the target empty block and the threat exposure penalty term within the empty block. When performing path search and deviation path pre-calculation, the above attributes are used as heuristic evaluation indicators to accelerate search convergence and reduce the probability of crossing high-threat areas.

3. The multi-machine four-dimensional collaborative path planning method based on pre-calculated deviation paths and dynamic replanning as described in claim 1, characterized in that: In step 3, the sampling and expansion process of the Dynamic Priority Fast Expanding Random Tree Algorithm (DPRRT*) introduces a priority scheduling mechanism based on task urgency and path coupling. This mechanism optimizes the shortcomings of the traditional DPRRT* algorithm, which relies only on a single-dimensional priority and does not consider the path coupling characteristics of multiple drones. Specifically, it first integrates task urgency and path coupling into the core priority evaluation index, replacing the traditional single priority determination method, and prioritizes allocating better path resources to drones with high path coupling and tight remaining time.

4. The multi-machine four-dimensional collaborative path planning method based on pre-calculated deviation paths and dynamic replanning as described in claim 1, characterized in that: The K-shortest path algorithm is improved as follows: The improved K-shortest path algorithm is based on the traditional Yen algorithm. Addressing its shortcomings—repeatedly calculating path segments, generating all branches, lacking targeted pruning, using only geometric length as the cost metric, failing to consider multi-machine path conflicts, and only outputting path sequences—it utilizes reusable path segments in the reverse reachability graph, calculates local branches using Dijkstra's algorithm and concatenates them with the initial reverse path, double-prunes empty blocks not in the reverse reachability graph, and calculates the comprehensive cost by combining geometric length, cooperative arrival time deviation weights, and threat exposure penalties. It also adds inter-machine spatiotemporal conflict verification and stores path options containing key information such as empty block indices and estimated arrival times. Finally, it selects the top K optimal paths and stores them in corresponding empty blocks. Simultaneously, it reduces the pre-computation time complexity from the quadratic of the number of nodes to the product of the number of candidate paths and the average neighborhood size.

5. The multi-machine four-dimensional collaborative path planning method for pre-calculated deviation paths and dynamic replanning according to claim 1, characterized in that: The improved K-shortest path algorithm is used to obtain K off-paths as follows: First, using the constructed reverse reachability graph, the reusable path segments of each empty block recorded therein are directly called; Secondly, for each selected candidate empty block, the local branch path to the next reverse path point is calculated using Dijkstra's algorithm, and then spliced ​​with the remaining part of the reverse initial path to form a complete deviation path. Finally, the complexity is reduced by double pruning optimization. Finally, the comprehensive cost is calculated by combining the geometric path length, the weight of the cooperative arrival reference time deviation, and the threat exposure penalty term through the comprehensive cost function. At the same time, the spatiotemporal conflict between the path and the initial paths of other UAVs is checked to meet the inter-UAV safety constraints. The top K deviation paths with the minimum cost are selected as candidate path options and stored in the option set of the corresponding empty block.

6. The multi-machine four-dimensional collaborative path planning method based on pre-calculated deviation paths and dynamic replanning as described in claim 1, characterized in that: The heuristic artificial potential field algorithm IHAPF is improved as follows: Based on the traditional artificial potential field algorithm, the gravitational potential field direction is first optimized by adjusting the gravitational target from a distant empty block to the next reference path point of the initial path in step 3. Secondly, an adaptive repulsive potential field is designed, with the magnitude of the repulsive force dynamically adjusted according to the distance between the UAV and the dynamic threat. The closer the distance, the greater the repulsive force. After exceeding the safe range, the repulsive force decays to 0, solving the problem that traditional algorithms are prone to getting trapped in local minima. Next, a pre-stored path guidance constraint is embedded, which prioritizes driving the UAV to move towards the empty block with the pre-stored deviation path option in step 5 during obstacle avoidance, ensuring that pre-stored resources can be directly called after obstacle avoidance. Finally, a time coordination constraint is added to strictly control the flight time of the obstacle avoidance segment within the tolerance range of the coordinated arrival reference time, avoiding time deviations in subsequent path splicing.

Images